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3 years ago

-4/9 multiplied by -5/8

1 answer:

7 0

To multiply fractions, multiply the two numerators and then the two denominators together.

-4*-5=20
8*9=72

20/72=
10/36=
5/18

Final answer: 5/18

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Write 9x² - 36x = 4y² + 24y + 36 in standard form

Kisachek [45]

Answer:

9·x² - 36·x = 4·y² + 24·y + 36 in standard form is;

(x - 2)²/2² - (y + 3)²/3² = 1

Step-by-step explanation:

The standard form of a hyperbola is given as follows;

(x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/b² - (x - h)²/a² = 1

The given equation is presented as follows;

9·x² - 36·x = 4·y² + 24·y + 36

By completing the square, we get;

(3·x - 6)·(3·x - 6) - 36 = (2·y + 6)·(2·y + 6)

(3·x - 6)² - 36 = (2·y + 6)²

(3·x - 6)² - (2·y + 6)² = 36

(3·x - 6)²/36 - (2·y + 6)²/36 = 36/36 = 1

(3·x - 6)²/6² - (2·y + 6)²/6² = 1

3²·(x - 2)²/6² - 2²·(y + 3)²/6² = 1

(x - 2)²/2² - (y + 3)²/3² = 1

The equation of the hyperbola is (x - 2)²/2² - (y + 3)²/3² = 1.

5 0

3 years ago

a vehicle uses 1 1/8 gallons of gas to travel 13 1/2 miles. at this rate how many miles can the vehicle travel per gallon of gas

elena55 [62]

Answer:

The vehicle can travel 12 miles per gallon of gas.

Step-by-step explanation:

The number of gallons used by a vehicle = 1 1/8 gallons

i.e.

$1\frac{1}{8}=\frac{9}{8}$ gallons

The number of miles traveled by a vehicle = 13 1/2 miles

i.e.

$13\frac{1}{2}=\frac{27}{2}$ miles

Thus,

Total Gallons =9/8 gallons

Total Distance in miles = 27/2 miles

Hence:

Unit Rate = [27/2 miles] / [9/8 gallons]

= 12 miles per gallons ∵ $\frac{27}{2}\div \frac{9}{8}=12$

Therefore, the vehicle can travel 12 miles per gallon of gas.

8 0

3 years ago

1 point) Are the functions f,g, and h given below linearly independent? f(x)=e3x+cos(5x), g(x)=e3x−cos(5x), h(x)=cos(5x). If the

Fynjy0 [20]

Answer:

Functions are linearly dependent (are not linearly independent.)

Step-by-step explanation:

Remember that two functions f(x), g(x) and h(x) are said linearly independent on an interval I if the <em>only solution</em> to the equation

$\alpha f(x)+\beta g(x)+\omega h(x)=0, \ \text{for all } x\in I$

is the trivial one: α = 0, β = 0, ω = 0. If they are not linearly independent, they are called linearly dependent.

Now, let f(x), g(x) and h(x) be the functions:

$f(x)=e^{3x}+\cos(5x),$

$g(x)=e^{3x}-\cos(5x),$

$h(x)=\cos(5x).$

Then, letting α = 1, β= -1 and ω = -2, we see that:

$\alpha f(x)+\beta g(x)+ \omega h(x)=e^{3x}+\cos(5x)-e^{3x}+\cos(5x)+2\cos(5x)=0.$

Hence, the functions f(x), g(x) and h(x) are not linearly independent, or equivalently, are linearly dependent.

8 0

3 years ago

Please help thank you

sammy [17]

Learn the common vocabulary for multiplication, division, subtraction and addition it will help you understand what they mean in the written expression

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3 years ago

All geometric figures,shapes,and solids can be named using sets of

Naddika [18.5K]

Answer:

All geometric figures, shapes and solids can be named as a sets of surface regions and plane regions and they all lie in three dimensional spaces.

Step-by-step explanation:

7 0

3 years ago